Question

Select the expression that represents the simplified product.

Given:
F(x)=x+2 and G(x)=3x+5
Find (F⋅G)(x)

3x2+11x+10

14x2+10

3x2+10x+10

Answer 1

Here you go! Hope this helps

Answer 2

`(FxG)(x)=3x^2+11x+10`.

Explanation:

This is a simple multiplication of functions. In order to get a result, we must find the product generated by the multiplication of the arguments of both functions.

1. Write the arguments.

`F(x)= x+2\\ \\G(x)=3x+5`

2. Multiply the arguments.

`(x+2)(3x+5)`

Using the associative property of multiplication, rewrite the expression.

This is the rule we are applying:
`(a+b)(c+d)=(a)(c)+(a)(d)+(b)(c)+(b)(d)`

Rewriting:

`(x)(3x)+(x)(5)+(2)(3x)+(2)(5)\\ \\(3x^2)+(5x)+(6x)+(10)\\\\3x^2+11x+10`

3. Express your result.

`(FxG)(x)=3x^2+11x+10`.